Cytokinesis is the process ending the cell cycle in which the mother cell cytoplasm divides into two. As a critical step in cell division it is fundamentally important to life and defects in the process are associated with cancer, neurological disease and birth defects. Animals and fungi accomplish cytokinesis by constriction of an actomyosin contractile ring built from force-producing myosin motor proteins, actin filaments and other com- ponents. While much is established about the molecular parts it remains much less clear how these parts coordinate to produce a functional contractile machine. This has been difficult because experimentally mea- suring how the parts are spatiotemporally organized is challenging and mathematical modeling is needed to translate hypothesized arrangements into key observables such as ring constriction rate. This research project is a program of mathematical modeling and computational simulation focusing on fission yeast as a model sys- tem to establish principles of cytokinesis which may be general since many proteins involved are conserved between yeast and animals. The modeling will proceed as part of a tight theory-experiment collaboration with an experimental colleague studying yeast cytokinesis. A 3-phase strategy of increasing complexity will be adopted, starting with a simpler contractile system and ending with the full complexity of yeast constriction which occurs concomitantly with septation, the deposition of cell wall material between daughter cells. Phase A will consist in a study of stationary mammalian cell stress fibers, contractile actomyosin structures important in wound healing and other contexts. Stress fibers are relatively well characterized and their kinetics have been directly measured. Phase B will address yeast protoplasts, cells lacking cell wall in which ring constric- tion can occur without the complication of septation. In phase C constriction-septation in wild type yeast will be studied. The long term goals are to establish mechanisms of contractile force generation and kinetics in stress fibers and the fission yeast contractile ring and to determine the commonality between these systems. The specific aims of the modeling are: (i) To test hypothetical arrangements and turnover rules of actin, myosin, actin nucleators/depolymerization agents and other key components. In particular, to determine whether ar- rangements are sarcomeric (periodic, muscle-like) or non-sarcomeric (random) in the ring and stress fibers. (ii) To test the hypothesis that actin turnover is regulated by internal stresses. (iii) To apply models to predict outcomes of laser ablation experiments and spontaneous severing events which can reveal otherwise hidden features of actomyosin structures. Laser ablation experiments have already been performed on stress fibers. (iv) To test the hypothesis that the ring regulates septum growth in wild type yeast constriction. These aims will be accomplished by modeling efforts in a continuous dialog with experiments aiming to reveal new structural and kinetic features of the cytokinetic contractile ring.